Finite Group Databasebeta

← #14652856

Subgroups — #14652856

Order 2816.

538 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077012C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic
3#13068471C211yesmaximal, characteristic
4C2×#10622120C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6C2×#10622124C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66997—22no—
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66879—21no—
14#10622589—21no—
15#10622589—21no—
16#10622589C414yes—
17C42×Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#332—22no—
21#10622188—21no—
22#10622188—22no—
23#10622185—22no—
24#10622124—22no—
25#10622120—22no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C42×C11C2311yescharacteristic
37#66997—44no—
38#66997—44no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C412yes—
41C2×Dic11⋊C4—24no—
42C2×Dic11⋊C4—24no—
43C2×C4×Dic11C2×C412yes—
44C2×C4×Dic11D412yes—
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57#66879—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62#9703—111nomaximal, Sylow
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11—42no—
66C2×Q8×C11—42no—
67C22×C4×C11—22no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11C22⋊C412yes—
73C22×Dic11C22⋊C412yes—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—42no—
77C2×Dic22—42no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—42no—
82C2×C8×C11—41no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—48no—
96Dic11⋊C4—48no—
97C4×Dic11—24no—
98C4×Dic11—22no—
99C4×Dic11—22no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11SD1612yes—
103C4×Dic11Q1612yes—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—42no—
108C2×C11⋊C8—41no—
109#2868—111no—
110#1831—111no—
111#1767—111no—
112C2×#332—111no—
113C2×#332—111no—
114C2×#332—111no—
115C2×#332D1111yescharacteristic
116C23×C11C2×C22⋊C411yescharacteristic
117Q8×C11—82no—
118Q8×C11—81no—
119Q8×C11—81no—
120C2×C4×C11—22no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12411yescharacteristic
128C2×C4×C11#12711yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)12yes—
132C2×C4×C11AGL(1,ℤ/8)12yes—
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—22no—
139C2×Dic11—42no—
140C2×Dic11—44no—
141C2×Dic11#10114yes—
142C2×Dic11#10314yes—
143Dic22—82no—
144Dic22—81no—
145Dic22—81no—
146C8×C11—42no—
147C8×C11—81no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150C2×C4⋊Q8—111no—
151C2×C4⋊Q8—222no—
152C2×C4⋊Q8C2×D1111yescharacteristic
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
155C2×C4⋊C8C2×D1111yescharacteristic
156C2×C4⋊C8C2×D1111yescharacteristic
157C2×#97—221no—
158#384—114no—
159#384—221no—
160#384—221no—
161C43—111no—
162#336—222no—
163#336—221no—
164#332—22no—
165#332—222no—
166#332—222no—
167#332—222no—
168C22×C11#39011yescharacteristic
169C22×C11C2×#10112yes—
170C22×C11C2×#10311yescharacteristic
171C22×C11#41812yes—
172C22×C11#41911yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11#46111yescharacteristic
177C4×C11#46111yescharacteristic
178C4×C11#46211yescharacteristic
179C4×C11#46211yescharacteristic
180C4×C11#49012yes—
181C4×C11#49611yescharacteristic
182C4×C11#49611yescharacteristic
183Dic11—24no—
184Dic11—24no—
185Dic11—82no—
186C22×Q8—21no—
187C22×Q8—221no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—221no—
191C22×C8—221no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—444no—
201C4⋊Q8—444no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—112no—
204C2×C4⋊C4—224no—
205C2×C4⋊C4—224no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C4×D1112yes—
208C2×C42—111no—
209C2×C42—112no—
210C2×C42—112no—
211C2×C42—111no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—112no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8C22⋊D1112yes—
221#97—442no—
222C2×C11#154912yes—
223C2×C11#155612yes—
224C2×C11#196111yescharacteristic
225C2×C11#196611yescharacteristic
226C2×C11#198111yescharacteristic
227C2×Q8—41no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—441no—
232C2×Q8—442no—
233C2×Q8—442no—
234C2×Q8—441no—
235C22×C4—22no—
236C22×C4—112no—
237C22×C4—112no—
238C22×C4—222no—
239C22×C4C2×C4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—42no—
246C2×C8—41no—
247C2×C8—222no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—442no—
251C2×C8—441no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—448no—
259C4⋊C4—448no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C42—112no—
263C42—112no—
264C42—224no—
265C42—222no—
266C42—222no—
267C42—221no—
268C42—221no—
269C42#433911yescharacteristic
270C42D4×D1111yescharacteristic
271C42#434111yescharacteristic
272C42C2×C22⋊D1111yescharacteristic
273C11#970311yescharacteristic, complemented, Sylow
274C23C22⋊C4×D1111yescharacteristic
275Q8—81no—
276Q8—81no—
277Q8—82no—
278Q8—881no—
279Q8—881no—
280Q8—882no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—114no—
285C2×C4—114no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—442no—
291C2×C4—444no—
292C2×C4(C22⋊D11)⋊C411yescharacteristic
293C2×C4#6693711yescharacteristic
294C2×C4#6693811yescharacteristic
295C2×C4#6696412yes—
296C2×C4SD16×D1111yescharacteristic
297C2×C4#6696712yes—
298C2×C4#6696811yescharacteristic
299C2×C4Q16×D1111yescharacteristic
300C2×C4#6697111yescharacteristic
301C2×C4C4×C22⋊D1111yescharacteristic
302C2×C4#6699211yescharacteristic
303C2×C4#6699311yescharacteristic
304C8—42no—
305C8—81no—
306C8—442no—
307C8—881no—
308C22D11×#10112yes—
309C22#1062238312yes—
310C22D11×#10311yescharacteristic
311C22#1062241511yescharacteristic
312C22#1062257011yescharacteristic
313C4—21no—
314C4—21no—
315C4—82no—
316C4—224no—
317C4—224no—
318C4—882no—
319C4#1062237712yes—
320C4#1062240611yescharacteristic
321C4#1062243111yescharacteristic
322C4#1062276711yescharacteristic
323C4#1062277511yescharacteristic
324C4#1062278911yescharacteristic
325C4#1062279511yescharacteristic
326C2#1306729912yes—
327C2#1306733112yes—
328C2#1306943811yescharacteristic
329C2#1306945811yescharacteristic
330C2#1306953711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9703
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
273. C11#9703semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130770122
#130687322
#130684712
C2×#106221202
C2×#106221852
C2×#106221242
C2×C11×#3322
#970311